Question
onsider the triangle to the right.
a. Write an equation that can be used to find the value of y.
b. What is mangle∠K?
Upper LL
Upper MM
Upper KK
56 degrees56°
left parenthesis 5 y minus 19 right parenthesis degrees(5y−19)°
Question content area bottom
Part 1
a. Write the equation below.
5 y minus 19 equals 565y−19=56
(Do not simplify. Do not combine like terms.)
Part 2
b. What is mangle∠K?
a. Write an equation that can be used to find the value of y.
b. What is mangle∠K?
Upper LL
Upper MM
Upper KK
56 degrees56°
left parenthesis 5 y minus 19 right parenthesis degrees(5y−19)°
Question content area bottom
Part 1
a. Write the equation below.
5 y minus 19 equals 565y−19=56
(Do not simplify. Do not combine like terms.)
Part 2
b. What is mangle∠K?
Answers
GPT-4o mini
To solve the problem, we first analyze the information presented:
1. It mentions the angle measure \( \angle K \) along with \( (5y - 19)^\circ \) and \( 56^\circ \).
2. Typically, in a triangle, the sum of the angles must equal \( 180^\circ \).
### Part 1:
We are tasked with writing an equation to find the value of \( y \). Considering the angle measures given and understanding that they are part of a triangle, we can use the equations provided.
To find \( y \), we can set up the equation as provided:
\[
5y - 19 = 56
\]
### Part 2:
To find \( \angle K \), we only need the expression for \( \angle K \) if we substitute the value of \( y \).
Starting with the equation we wrote:
1. **From the equation**:
\[
5y - 19 = 56
\]
2. **Solve for \( y \)**:
\[
5y = 56 + 19
\]
\[
5y = 75
\]
\[
y = 15
\]
3. **Finding \( \angle K \)**:
Now we substitute \( y \) back into \( \angle K \):
\[
\angle K = 5y - 19
\]
Substituting \( y = 15 \):
\[
\angle K = 5(15) - 19 = 75 - 19 = 56^\circ
\]
Thus:
- **The answer to Part 1 is**:
\[
5y - 19 = 56
\]
- **The answer to Part 2 is**:
\(\angle K = 56^\circ\)
1. It mentions the angle measure \( \angle K \) along with \( (5y - 19)^\circ \) and \( 56^\circ \).
2. Typically, in a triangle, the sum of the angles must equal \( 180^\circ \).
### Part 1:
We are tasked with writing an equation to find the value of \( y \). Considering the angle measures given and understanding that they are part of a triangle, we can use the equations provided.
To find \( y \), we can set up the equation as provided:
\[
5y - 19 = 56
\]
### Part 2:
To find \( \angle K \), we only need the expression for \( \angle K \) if we substitute the value of \( y \).
Starting with the equation we wrote:
1. **From the equation**:
\[
5y - 19 = 56
\]
2. **Solve for \( y \)**:
\[
5y = 56 + 19
\]
\[
5y = 75
\]
\[
y = 15
\]
3. **Finding \( \angle K \)**:
Now we substitute \( y \) back into \( \angle K \):
\[
\angle K = 5y - 19
\]
Substituting \( y = 15 \):
\[
\angle K = 5(15) - 19 = 75 - 19 = 56^\circ
\]
Thus:
- **The answer to Part 1 is**:
\[
5y - 19 = 56
\]
- **The answer to Part 2 is**:
\(\angle K = 56^\circ\)